Cycle LDPC code[1] 


An LDPC code whose parity-check matrix forms the incidence matrix of a graph, i.e., has weight-two columns.


The minimum distance of a cycle LDPC code is \(d\geq g/2\), where \(g\) is the girth of the code's Tanner graph [2; Remark 21.2.13].


Cycle codes are not asymptotically good [3].


Linear-time encoder [4].


Cycle LDPC codes have been proposed to be used for MIMO channels [5].



  • Margulis LDPC code — Margulis LDPC codes are examples of cycle codes for particular large-girth graphs [7].


S. Hakimi and J. Bredeson, “Graph theoretic error-correcting codes”, IEEE Transactions on Information Theory 14, 584 (1968) DOI
C. A. Kelley, "Codes over Graphs." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
L. Decreusefond and G. Zemor, “On the error-correcting capabilities of cycle codes of graphs”, Proceedings of 1994 IEEE International Symposium on Information Theory DOI
Jie Huang and Jinkang Zhu, “Linear time encoding of cycle GF(2/sup P)/ codes through graph analysis”, IEEE Communications Letters 10, 369 (2006) DOI
Ronghui Peng and Rong-Rong Chen, “Application of Nonbinary LDPC Cycle Codes to MIMO Channels”, IEEE Transactions on Wireless Communications 7, 2020 (2008) DOI
R. M. Tanner et al., “LDPC Block and Convolutional Codes Based on Circulant Matrices”, IEEE Transactions on Information Theory 50, 2966 (2004) DOI
G. Zémor, “On Cayley Graphs, Surface Codes, and the Limits of Homological Coding for Quantum Error Correction”, Lecture Notes in Computer Science 259 (2009) DOI
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Zoo Code ID: cycle_ldpc

Cite as:
“Cycle LDPC code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024.
@incollection{eczoo_cycle_ldpc, title={Cycle LDPC code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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“Cycle LDPC code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024.